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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 Aug 2010 06:21:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/20/t12822853966mnppip8nv9ozjy.htm/, Retrieved Wed, 08 May 2024 17:01:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79439, Retrieved Wed, 08 May 2024 17:01:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Tendeloo Willem MAR 201 A
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijreeks A Stap 32] [2010-08-20 06:21:42] [6b796205aa6c71fffca3ea7e892beea1] [Current]
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Dataseries X:
252
251
250
248
268
267
252
242
243
243
244
246
236
241
240
239
253
249
232
229
221
222
224
224
215
225
225
221
238
234
228
227
216
219
225
227
205
215
214
209
222
216
206
199
189
198
203
211
199
211
210
203
214
202
193
193
176
192
200
195
180
197
194
194
212
202
195
198
170
187
190
189
176
188
195
194
211
203
194
194
163
183
181
184
171
178
179
186
205
204
195
186
156
167
164
165
153
160
154
169
186
188
187
169
131
146
145
137
119
118
113
123
142
141
138
124
83
100
96
98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79439&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79439&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.738004770331473
beta0.00040330803731264
gamma0.993056849962919

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.738004770331473 \tabularnewline
beta & 0.00040330803731264 \tabularnewline
gamma & 0.993056849962919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79439&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.738004770331473[/C][/ROW]
[ROW][C]beta[/C][C]0.00040330803731264[/C][/ROW]
[ROW][C]gamma[/C][C]0.993056849962919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79439&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.738004770331473
beta0.00040330803731264
gamma0.993056849962919







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13236242.919871794872-6.91987179487191
14241242.844421905514-1.84442190551403
15240240.597462599674-0.597462599673577
16239239.603920712573-0.603920712572801
17253253.522099621085-0.522099621084777
18249249.542174152664-0.542174152664415
19232236.047272209696-4.0472722096963
20229222.7977198702166.20228012978382
21221227.864232117884-6.86423211788363
22222222.243886236117-0.243886236117390
23224222.7176479385791.28235206142091
24224225.693162468729-1.69316246872879
25215212.8801768025382.11982319746204
26225220.7943870684844.20561293151567
27225223.3364232447601.66357675523960
28221224.010143754598-3.01014375459798
29238236.1733750948421.82662490515762
30234233.9218643165520.0781356834476696
31228219.9732633787478.026736621253
32227218.3051223755008.6948776245005
33216221.816376499747-5.81637649974658
34219218.6969090858730.303090914127239
35225219.9766960245725.02330397542829
36227224.9452691194082.05473088059222
37205215.897786261591-10.8977862615910
38215214.7512284818300.248771518170344
39214213.7141589630020.285841036997965
40209212.157142571301-3.15714257130097
41222225.472285489058-3.47228548905818
42216218.855646691196-2.85564669119628
43206204.8094719306101.19052806938979
44199198.2675111281000.732488871900472
45189192.122132444236-3.12213244423609
46198192.5791018497075.42089815029325
47203198.8613974562914.13860254370923
48211202.4018970249548.59810297504623
49199194.8126577294914.18734227050911
50211207.7026952088543.2973047911463
51210208.9296396374371.07036036256309
52203207.060590756305-4.06059075630466
53214219.631493776482-5.63149377648202
54202211.585642847658-9.58564284765825
55193193.627273055343-0.627273055342613
56193185.6259104509937.37408954900675
57176183.382475992651-7.38247599265094
58192182.9200081526889.07999184731176
59200191.5722224668778.42777753312319
60195199.442798816816-4.4427988168157
61180181.082244973198-1.08224497319770
62197189.8506748958647.14932510413558
63194193.3411168725940.658883127405545
64194189.8334082353824.16659176461792
65212208.0697120088873.93028799111335
66202206.056984643891-4.05698464389053
67195194.5164490950780.483550904921998
68198189.4238781644078.57612183559323
69170184.235835039232-14.2358350392324
70187183.0042495910433.99575040895664
71190187.7386180016232.26138199837669
72189187.7119516913811.28804830861864
73176174.4590358578981.54096414210173
74188187.3097551819680.690244818031886
75195184.34747462805210.6525253719483
76194189.1334861216034.86651387839723
77211207.8308057997613.16919420023930
78203203.184013802688-0.184013802688412
79194195.689965184857-1.68996518485685
80194191.1050529708362.89494702916429
81163175.793687440199-12.7936874401987
82183180.3748058788612.62519412113912
83181183.651016198034-2.6510161980344
84184179.7488365192654.25116348073493
85171168.7524965923522.24750340764831
86178181.907498781423-3.90749878142293
87179178.1468313066620.853168693337778
88186174.19539378932811.8046062106716
89205197.5734268718517.42657312814865
90204195.1994135174008.80058648259953
91195193.9501417894951.04985821050511
92186192.586844307124-6.58684430712441
93156166.199967869213-10.1999678692126
94167176.711566047109-9.71156604710868
95164169.511449397-5.51144939700015
96165165.294192582807-0.294192582807284
97153150.4208543484262.57914565157353
98160162.218124716795-2.21812471679536
99154160.942237802094-6.9422378020939
100169154.084138057314.9158619426998
101186178.6172409520357.38275904796515
102188176.56637313630711.4336268636928
103187175.24252180134911.7574781986509
104169179.796576813874-10.7965768138739
105131149.363561882391-18.3635618823906
106146153.975742189308-7.97574218930825
107145149.148241638383-4.1482416383835
108137147.293649833780-10.2936498337796
109119125.784467627682-6.7844676276823
110118129.416653420513-11.4166534205128
111113120.113811035301-7.1138110353006
112123118.8066989426344.19330105736555
113142133.4540286061238.54597139387727
114141133.3033641130047.6966358869957
115138129.2925495559858.70745044401522
116124125.713429896508-1.71342989650771
11783100.003562887558-17.0035628875582
118100108.310988013908-8.3109880139077
11996104.220695108887-8.22069510888707
1209897.74930866496630.250691335033650

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 236 & 242.919871794872 & -6.91987179487191 \tabularnewline
14 & 241 & 242.844421905514 & -1.84442190551403 \tabularnewline
15 & 240 & 240.597462599674 & -0.597462599673577 \tabularnewline
16 & 239 & 239.603920712573 & -0.603920712572801 \tabularnewline
17 & 253 & 253.522099621085 & -0.522099621084777 \tabularnewline
18 & 249 & 249.542174152664 & -0.542174152664415 \tabularnewline
19 & 232 & 236.047272209696 & -4.0472722096963 \tabularnewline
20 & 229 & 222.797719870216 & 6.20228012978382 \tabularnewline
21 & 221 & 227.864232117884 & -6.86423211788363 \tabularnewline
22 & 222 & 222.243886236117 & -0.243886236117390 \tabularnewline
23 & 224 & 222.717647938579 & 1.28235206142091 \tabularnewline
24 & 224 & 225.693162468729 & -1.69316246872879 \tabularnewline
25 & 215 & 212.880176802538 & 2.11982319746204 \tabularnewline
26 & 225 & 220.794387068484 & 4.20561293151567 \tabularnewline
27 & 225 & 223.336423244760 & 1.66357675523960 \tabularnewline
28 & 221 & 224.010143754598 & -3.01014375459798 \tabularnewline
29 & 238 & 236.173375094842 & 1.82662490515762 \tabularnewline
30 & 234 & 233.921864316552 & 0.0781356834476696 \tabularnewline
31 & 228 & 219.973263378747 & 8.026736621253 \tabularnewline
32 & 227 & 218.305122375500 & 8.6948776245005 \tabularnewline
33 & 216 & 221.816376499747 & -5.81637649974658 \tabularnewline
34 & 219 & 218.696909085873 & 0.303090914127239 \tabularnewline
35 & 225 & 219.976696024572 & 5.02330397542829 \tabularnewline
36 & 227 & 224.945269119408 & 2.05473088059222 \tabularnewline
37 & 205 & 215.897786261591 & -10.8977862615910 \tabularnewline
38 & 215 & 214.751228481830 & 0.248771518170344 \tabularnewline
39 & 214 & 213.714158963002 & 0.285841036997965 \tabularnewline
40 & 209 & 212.157142571301 & -3.15714257130097 \tabularnewline
41 & 222 & 225.472285489058 & -3.47228548905818 \tabularnewline
42 & 216 & 218.855646691196 & -2.85564669119628 \tabularnewline
43 & 206 & 204.809471930610 & 1.19052806938979 \tabularnewline
44 & 199 & 198.267511128100 & 0.732488871900472 \tabularnewline
45 & 189 & 192.122132444236 & -3.12213244423609 \tabularnewline
46 & 198 & 192.579101849707 & 5.42089815029325 \tabularnewline
47 & 203 & 198.861397456291 & 4.13860254370923 \tabularnewline
48 & 211 & 202.401897024954 & 8.59810297504623 \tabularnewline
49 & 199 & 194.812657729491 & 4.18734227050911 \tabularnewline
50 & 211 & 207.702695208854 & 3.2973047911463 \tabularnewline
51 & 210 & 208.929639637437 & 1.07036036256309 \tabularnewline
52 & 203 & 207.060590756305 & -4.06059075630466 \tabularnewline
53 & 214 & 219.631493776482 & -5.63149377648202 \tabularnewline
54 & 202 & 211.585642847658 & -9.58564284765825 \tabularnewline
55 & 193 & 193.627273055343 & -0.627273055342613 \tabularnewline
56 & 193 & 185.625910450993 & 7.37408954900675 \tabularnewline
57 & 176 & 183.382475992651 & -7.38247599265094 \tabularnewline
58 & 192 & 182.920008152688 & 9.07999184731176 \tabularnewline
59 & 200 & 191.572222466877 & 8.42777753312319 \tabularnewline
60 & 195 & 199.442798816816 & -4.4427988168157 \tabularnewline
61 & 180 & 181.082244973198 & -1.08224497319770 \tabularnewline
62 & 197 & 189.850674895864 & 7.14932510413558 \tabularnewline
63 & 194 & 193.341116872594 & 0.658883127405545 \tabularnewline
64 & 194 & 189.833408235382 & 4.16659176461792 \tabularnewline
65 & 212 & 208.069712008887 & 3.93028799111335 \tabularnewline
66 & 202 & 206.056984643891 & -4.05698464389053 \tabularnewline
67 & 195 & 194.516449095078 & 0.483550904921998 \tabularnewline
68 & 198 & 189.423878164407 & 8.57612183559323 \tabularnewline
69 & 170 & 184.235835039232 & -14.2358350392324 \tabularnewline
70 & 187 & 183.004249591043 & 3.99575040895664 \tabularnewline
71 & 190 & 187.738618001623 & 2.26138199837669 \tabularnewline
72 & 189 & 187.711951691381 & 1.28804830861864 \tabularnewline
73 & 176 & 174.459035857898 & 1.54096414210173 \tabularnewline
74 & 188 & 187.309755181968 & 0.690244818031886 \tabularnewline
75 & 195 & 184.347474628052 & 10.6525253719483 \tabularnewline
76 & 194 & 189.133486121603 & 4.86651387839723 \tabularnewline
77 & 211 & 207.830805799761 & 3.16919420023930 \tabularnewline
78 & 203 & 203.184013802688 & -0.184013802688412 \tabularnewline
79 & 194 & 195.689965184857 & -1.68996518485685 \tabularnewline
80 & 194 & 191.105052970836 & 2.89494702916429 \tabularnewline
81 & 163 & 175.793687440199 & -12.7936874401987 \tabularnewline
82 & 183 & 180.374805878861 & 2.62519412113912 \tabularnewline
83 & 181 & 183.651016198034 & -2.6510161980344 \tabularnewline
84 & 184 & 179.748836519265 & 4.25116348073493 \tabularnewline
85 & 171 & 168.752496592352 & 2.24750340764831 \tabularnewline
86 & 178 & 181.907498781423 & -3.90749878142293 \tabularnewline
87 & 179 & 178.146831306662 & 0.853168693337778 \tabularnewline
88 & 186 & 174.195393789328 & 11.8046062106716 \tabularnewline
89 & 205 & 197.573426871851 & 7.42657312814865 \tabularnewline
90 & 204 & 195.199413517400 & 8.80058648259953 \tabularnewline
91 & 195 & 193.950141789495 & 1.04985821050511 \tabularnewline
92 & 186 & 192.586844307124 & -6.58684430712441 \tabularnewline
93 & 156 & 166.199967869213 & -10.1999678692126 \tabularnewline
94 & 167 & 176.711566047109 & -9.71156604710868 \tabularnewline
95 & 164 & 169.511449397 & -5.51144939700015 \tabularnewline
96 & 165 & 165.294192582807 & -0.294192582807284 \tabularnewline
97 & 153 & 150.420854348426 & 2.57914565157353 \tabularnewline
98 & 160 & 162.218124716795 & -2.21812471679536 \tabularnewline
99 & 154 & 160.942237802094 & -6.9422378020939 \tabularnewline
100 & 169 & 154.0841380573 & 14.9158619426998 \tabularnewline
101 & 186 & 178.617240952035 & 7.38275904796515 \tabularnewline
102 & 188 & 176.566373136307 & 11.4336268636928 \tabularnewline
103 & 187 & 175.242521801349 & 11.7574781986509 \tabularnewline
104 & 169 & 179.796576813874 & -10.7965768138739 \tabularnewline
105 & 131 & 149.363561882391 & -18.3635618823906 \tabularnewline
106 & 146 & 153.975742189308 & -7.97574218930825 \tabularnewline
107 & 145 & 149.148241638383 & -4.1482416383835 \tabularnewline
108 & 137 & 147.293649833780 & -10.2936498337796 \tabularnewline
109 & 119 & 125.784467627682 & -6.7844676276823 \tabularnewline
110 & 118 & 129.416653420513 & -11.4166534205128 \tabularnewline
111 & 113 & 120.113811035301 & -7.1138110353006 \tabularnewline
112 & 123 & 118.806698942634 & 4.19330105736555 \tabularnewline
113 & 142 & 133.454028606123 & 8.54597139387727 \tabularnewline
114 & 141 & 133.303364113004 & 7.6966358869957 \tabularnewline
115 & 138 & 129.292549555985 & 8.70745044401522 \tabularnewline
116 & 124 & 125.713429896508 & -1.71342989650771 \tabularnewline
117 & 83 & 100.003562887558 & -17.0035628875582 \tabularnewline
118 & 100 & 108.310988013908 & -8.3109880139077 \tabularnewline
119 & 96 & 104.220695108887 & -8.22069510888707 \tabularnewline
120 & 98 & 97.7493086649663 & 0.250691335033650 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79439&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]236[/C][C]242.919871794872[/C][C]-6.91987179487191[/C][/ROW]
[ROW][C]14[/C][C]241[/C][C]242.844421905514[/C][C]-1.84442190551403[/C][/ROW]
[ROW][C]15[/C][C]240[/C][C]240.597462599674[/C][C]-0.597462599673577[/C][/ROW]
[ROW][C]16[/C][C]239[/C][C]239.603920712573[/C][C]-0.603920712572801[/C][/ROW]
[ROW][C]17[/C][C]253[/C][C]253.522099621085[/C][C]-0.522099621084777[/C][/ROW]
[ROW][C]18[/C][C]249[/C][C]249.542174152664[/C][C]-0.542174152664415[/C][/ROW]
[ROW][C]19[/C][C]232[/C][C]236.047272209696[/C][C]-4.0472722096963[/C][/ROW]
[ROW][C]20[/C][C]229[/C][C]222.797719870216[/C][C]6.20228012978382[/C][/ROW]
[ROW][C]21[/C][C]221[/C][C]227.864232117884[/C][C]-6.86423211788363[/C][/ROW]
[ROW][C]22[/C][C]222[/C][C]222.243886236117[/C][C]-0.243886236117390[/C][/ROW]
[ROW][C]23[/C][C]224[/C][C]222.717647938579[/C][C]1.28235206142091[/C][/ROW]
[ROW][C]24[/C][C]224[/C][C]225.693162468729[/C][C]-1.69316246872879[/C][/ROW]
[ROW][C]25[/C][C]215[/C][C]212.880176802538[/C][C]2.11982319746204[/C][/ROW]
[ROW][C]26[/C][C]225[/C][C]220.794387068484[/C][C]4.20561293151567[/C][/ROW]
[ROW][C]27[/C][C]225[/C][C]223.336423244760[/C][C]1.66357675523960[/C][/ROW]
[ROW][C]28[/C][C]221[/C][C]224.010143754598[/C][C]-3.01014375459798[/C][/ROW]
[ROW][C]29[/C][C]238[/C][C]236.173375094842[/C][C]1.82662490515762[/C][/ROW]
[ROW][C]30[/C][C]234[/C][C]233.921864316552[/C][C]0.0781356834476696[/C][/ROW]
[ROW][C]31[/C][C]228[/C][C]219.973263378747[/C][C]8.026736621253[/C][/ROW]
[ROW][C]32[/C][C]227[/C][C]218.305122375500[/C][C]8.6948776245005[/C][/ROW]
[ROW][C]33[/C][C]216[/C][C]221.816376499747[/C][C]-5.81637649974658[/C][/ROW]
[ROW][C]34[/C][C]219[/C][C]218.696909085873[/C][C]0.303090914127239[/C][/ROW]
[ROW][C]35[/C][C]225[/C][C]219.976696024572[/C][C]5.02330397542829[/C][/ROW]
[ROW][C]36[/C][C]227[/C][C]224.945269119408[/C][C]2.05473088059222[/C][/ROW]
[ROW][C]37[/C][C]205[/C][C]215.897786261591[/C][C]-10.8977862615910[/C][/ROW]
[ROW][C]38[/C][C]215[/C][C]214.751228481830[/C][C]0.248771518170344[/C][/ROW]
[ROW][C]39[/C][C]214[/C][C]213.714158963002[/C][C]0.285841036997965[/C][/ROW]
[ROW][C]40[/C][C]209[/C][C]212.157142571301[/C][C]-3.15714257130097[/C][/ROW]
[ROW][C]41[/C][C]222[/C][C]225.472285489058[/C][C]-3.47228548905818[/C][/ROW]
[ROW][C]42[/C][C]216[/C][C]218.855646691196[/C][C]-2.85564669119628[/C][/ROW]
[ROW][C]43[/C][C]206[/C][C]204.809471930610[/C][C]1.19052806938979[/C][/ROW]
[ROW][C]44[/C][C]199[/C][C]198.267511128100[/C][C]0.732488871900472[/C][/ROW]
[ROW][C]45[/C][C]189[/C][C]192.122132444236[/C][C]-3.12213244423609[/C][/ROW]
[ROW][C]46[/C][C]198[/C][C]192.579101849707[/C][C]5.42089815029325[/C][/ROW]
[ROW][C]47[/C][C]203[/C][C]198.861397456291[/C][C]4.13860254370923[/C][/ROW]
[ROW][C]48[/C][C]211[/C][C]202.401897024954[/C][C]8.59810297504623[/C][/ROW]
[ROW][C]49[/C][C]199[/C][C]194.812657729491[/C][C]4.18734227050911[/C][/ROW]
[ROW][C]50[/C][C]211[/C][C]207.702695208854[/C][C]3.2973047911463[/C][/ROW]
[ROW][C]51[/C][C]210[/C][C]208.929639637437[/C][C]1.07036036256309[/C][/ROW]
[ROW][C]52[/C][C]203[/C][C]207.060590756305[/C][C]-4.06059075630466[/C][/ROW]
[ROW][C]53[/C][C]214[/C][C]219.631493776482[/C][C]-5.63149377648202[/C][/ROW]
[ROW][C]54[/C][C]202[/C][C]211.585642847658[/C][C]-9.58564284765825[/C][/ROW]
[ROW][C]55[/C][C]193[/C][C]193.627273055343[/C][C]-0.627273055342613[/C][/ROW]
[ROW][C]56[/C][C]193[/C][C]185.625910450993[/C][C]7.37408954900675[/C][/ROW]
[ROW][C]57[/C][C]176[/C][C]183.382475992651[/C][C]-7.38247599265094[/C][/ROW]
[ROW][C]58[/C][C]192[/C][C]182.920008152688[/C][C]9.07999184731176[/C][/ROW]
[ROW][C]59[/C][C]200[/C][C]191.572222466877[/C][C]8.42777753312319[/C][/ROW]
[ROW][C]60[/C][C]195[/C][C]199.442798816816[/C][C]-4.4427988168157[/C][/ROW]
[ROW][C]61[/C][C]180[/C][C]181.082244973198[/C][C]-1.08224497319770[/C][/ROW]
[ROW][C]62[/C][C]197[/C][C]189.850674895864[/C][C]7.14932510413558[/C][/ROW]
[ROW][C]63[/C][C]194[/C][C]193.341116872594[/C][C]0.658883127405545[/C][/ROW]
[ROW][C]64[/C][C]194[/C][C]189.833408235382[/C][C]4.16659176461792[/C][/ROW]
[ROW][C]65[/C][C]212[/C][C]208.069712008887[/C][C]3.93028799111335[/C][/ROW]
[ROW][C]66[/C][C]202[/C][C]206.056984643891[/C][C]-4.05698464389053[/C][/ROW]
[ROW][C]67[/C][C]195[/C][C]194.516449095078[/C][C]0.483550904921998[/C][/ROW]
[ROW][C]68[/C][C]198[/C][C]189.423878164407[/C][C]8.57612183559323[/C][/ROW]
[ROW][C]69[/C][C]170[/C][C]184.235835039232[/C][C]-14.2358350392324[/C][/ROW]
[ROW][C]70[/C][C]187[/C][C]183.004249591043[/C][C]3.99575040895664[/C][/ROW]
[ROW][C]71[/C][C]190[/C][C]187.738618001623[/C][C]2.26138199837669[/C][/ROW]
[ROW][C]72[/C][C]189[/C][C]187.711951691381[/C][C]1.28804830861864[/C][/ROW]
[ROW][C]73[/C][C]176[/C][C]174.459035857898[/C][C]1.54096414210173[/C][/ROW]
[ROW][C]74[/C][C]188[/C][C]187.309755181968[/C][C]0.690244818031886[/C][/ROW]
[ROW][C]75[/C][C]195[/C][C]184.347474628052[/C][C]10.6525253719483[/C][/ROW]
[ROW][C]76[/C][C]194[/C][C]189.133486121603[/C][C]4.86651387839723[/C][/ROW]
[ROW][C]77[/C][C]211[/C][C]207.830805799761[/C][C]3.16919420023930[/C][/ROW]
[ROW][C]78[/C][C]203[/C][C]203.184013802688[/C][C]-0.184013802688412[/C][/ROW]
[ROW][C]79[/C][C]194[/C][C]195.689965184857[/C][C]-1.68996518485685[/C][/ROW]
[ROW][C]80[/C][C]194[/C][C]191.105052970836[/C][C]2.89494702916429[/C][/ROW]
[ROW][C]81[/C][C]163[/C][C]175.793687440199[/C][C]-12.7936874401987[/C][/ROW]
[ROW][C]82[/C][C]183[/C][C]180.374805878861[/C][C]2.62519412113912[/C][/ROW]
[ROW][C]83[/C][C]181[/C][C]183.651016198034[/C][C]-2.6510161980344[/C][/ROW]
[ROW][C]84[/C][C]184[/C][C]179.748836519265[/C][C]4.25116348073493[/C][/ROW]
[ROW][C]85[/C][C]171[/C][C]168.752496592352[/C][C]2.24750340764831[/C][/ROW]
[ROW][C]86[/C][C]178[/C][C]181.907498781423[/C][C]-3.90749878142293[/C][/ROW]
[ROW][C]87[/C][C]179[/C][C]178.146831306662[/C][C]0.853168693337778[/C][/ROW]
[ROW][C]88[/C][C]186[/C][C]174.195393789328[/C][C]11.8046062106716[/C][/ROW]
[ROW][C]89[/C][C]205[/C][C]197.573426871851[/C][C]7.42657312814865[/C][/ROW]
[ROW][C]90[/C][C]204[/C][C]195.199413517400[/C][C]8.80058648259953[/C][/ROW]
[ROW][C]91[/C][C]195[/C][C]193.950141789495[/C][C]1.04985821050511[/C][/ROW]
[ROW][C]92[/C][C]186[/C][C]192.586844307124[/C][C]-6.58684430712441[/C][/ROW]
[ROW][C]93[/C][C]156[/C][C]166.199967869213[/C][C]-10.1999678692126[/C][/ROW]
[ROW][C]94[/C][C]167[/C][C]176.711566047109[/C][C]-9.71156604710868[/C][/ROW]
[ROW][C]95[/C][C]164[/C][C]169.511449397[/C][C]-5.51144939700015[/C][/ROW]
[ROW][C]96[/C][C]165[/C][C]165.294192582807[/C][C]-0.294192582807284[/C][/ROW]
[ROW][C]97[/C][C]153[/C][C]150.420854348426[/C][C]2.57914565157353[/C][/ROW]
[ROW][C]98[/C][C]160[/C][C]162.218124716795[/C][C]-2.21812471679536[/C][/ROW]
[ROW][C]99[/C][C]154[/C][C]160.942237802094[/C][C]-6.9422378020939[/C][/ROW]
[ROW][C]100[/C][C]169[/C][C]154.0841380573[/C][C]14.9158619426998[/C][/ROW]
[ROW][C]101[/C][C]186[/C][C]178.617240952035[/C][C]7.38275904796515[/C][/ROW]
[ROW][C]102[/C][C]188[/C][C]176.566373136307[/C][C]11.4336268636928[/C][/ROW]
[ROW][C]103[/C][C]187[/C][C]175.242521801349[/C][C]11.7574781986509[/C][/ROW]
[ROW][C]104[/C][C]169[/C][C]179.796576813874[/C][C]-10.7965768138739[/C][/ROW]
[ROW][C]105[/C][C]131[/C][C]149.363561882391[/C][C]-18.3635618823906[/C][/ROW]
[ROW][C]106[/C][C]146[/C][C]153.975742189308[/C][C]-7.97574218930825[/C][/ROW]
[ROW][C]107[/C][C]145[/C][C]149.148241638383[/C][C]-4.1482416383835[/C][/ROW]
[ROW][C]108[/C][C]137[/C][C]147.293649833780[/C][C]-10.2936498337796[/C][/ROW]
[ROW][C]109[/C][C]119[/C][C]125.784467627682[/C][C]-6.7844676276823[/C][/ROW]
[ROW][C]110[/C][C]118[/C][C]129.416653420513[/C][C]-11.4166534205128[/C][/ROW]
[ROW][C]111[/C][C]113[/C][C]120.113811035301[/C][C]-7.1138110353006[/C][/ROW]
[ROW][C]112[/C][C]123[/C][C]118.806698942634[/C][C]4.19330105736555[/C][/ROW]
[ROW][C]113[/C][C]142[/C][C]133.454028606123[/C][C]8.54597139387727[/C][/ROW]
[ROW][C]114[/C][C]141[/C][C]133.303364113004[/C][C]7.6966358869957[/C][/ROW]
[ROW][C]115[/C][C]138[/C][C]129.292549555985[/C][C]8.70745044401522[/C][/ROW]
[ROW][C]116[/C][C]124[/C][C]125.713429896508[/C][C]-1.71342989650771[/C][/ROW]
[ROW][C]117[/C][C]83[/C][C]100.003562887558[/C][C]-17.0035628875582[/C][/ROW]
[ROW][C]118[/C][C]100[/C][C]108.310988013908[/C][C]-8.3109880139077[/C][/ROW]
[ROW][C]119[/C][C]96[/C][C]104.220695108887[/C][C]-8.22069510888707[/C][/ROW]
[ROW][C]120[/C][C]98[/C][C]97.7493086649663[/C][C]0.250691335033650[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79439&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13236242.919871794872-6.91987179487191
14241242.844421905514-1.84442190551403
15240240.597462599674-0.597462599673577
16239239.603920712573-0.603920712572801
17253253.522099621085-0.522099621084777
18249249.542174152664-0.542174152664415
19232236.047272209696-4.0472722096963
20229222.7977198702166.20228012978382
21221227.864232117884-6.86423211788363
22222222.243886236117-0.243886236117390
23224222.7176479385791.28235206142091
24224225.693162468729-1.69316246872879
25215212.8801768025382.11982319746204
26225220.7943870684844.20561293151567
27225223.3364232447601.66357675523960
28221224.010143754598-3.01014375459798
29238236.1733750948421.82662490515762
30234233.9218643165520.0781356834476696
31228219.9732633787478.026736621253
32227218.3051223755008.6948776245005
33216221.816376499747-5.81637649974658
34219218.6969090858730.303090914127239
35225219.9766960245725.02330397542829
36227224.9452691194082.05473088059222
37205215.897786261591-10.8977862615910
38215214.7512284818300.248771518170344
39214213.7141589630020.285841036997965
40209212.157142571301-3.15714257130097
41222225.472285489058-3.47228548905818
42216218.855646691196-2.85564669119628
43206204.8094719306101.19052806938979
44199198.2675111281000.732488871900472
45189192.122132444236-3.12213244423609
46198192.5791018497075.42089815029325
47203198.8613974562914.13860254370923
48211202.4018970249548.59810297504623
49199194.8126577294914.18734227050911
50211207.7026952088543.2973047911463
51210208.9296396374371.07036036256309
52203207.060590756305-4.06059075630466
53214219.631493776482-5.63149377648202
54202211.585642847658-9.58564284765825
55193193.627273055343-0.627273055342613
56193185.6259104509937.37408954900675
57176183.382475992651-7.38247599265094
58192182.9200081526889.07999184731176
59200191.5722224668778.42777753312319
60195199.442798816816-4.4427988168157
61180181.082244973198-1.08224497319770
62197189.8506748958647.14932510413558
63194193.3411168725940.658883127405545
64194189.8334082353824.16659176461792
65212208.0697120088873.93028799111335
66202206.056984643891-4.05698464389053
67195194.5164490950780.483550904921998
68198189.4238781644078.57612183559323
69170184.235835039232-14.2358350392324
70187183.0042495910433.99575040895664
71190187.7386180016232.26138199837669
72189187.7119516913811.28804830861864
73176174.4590358578981.54096414210173
74188187.3097551819680.690244818031886
75195184.34747462805210.6525253719483
76194189.1334861216034.86651387839723
77211207.8308057997613.16919420023930
78203203.184013802688-0.184013802688412
79194195.689965184857-1.68996518485685
80194191.1050529708362.89494702916429
81163175.793687440199-12.7936874401987
82183180.3748058788612.62519412113912
83181183.651016198034-2.6510161980344
84184179.7488365192654.25116348073493
85171168.7524965923522.24750340764831
86178181.907498781423-3.90749878142293
87179178.1468313066620.853168693337778
88186174.19539378932811.8046062106716
89205197.5734268718517.42657312814865
90204195.1994135174008.80058648259953
91195193.9501417894951.04985821050511
92186192.586844307124-6.58684430712441
93156166.199967869213-10.1999678692126
94167176.711566047109-9.71156604710868
95164169.511449397-5.51144939700015
96165165.294192582807-0.294192582807284
97153150.4208543484262.57914565157353
98160162.218124716795-2.21812471679536
99154160.942237802094-6.9422378020939
100169154.084138057314.9158619426998
101186178.6172409520357.38275904796515
102188176.56637313630711.4336268636928
103187175.24252180134911.7574781986509
104169179.796576813874-10.7965768138739
105131149.363561882391-18.3635618823906
106146153.975742189308-7.97574218930825
107145149.148241638383-4.1482416383835
108137147.293649833780-10.2936498337796
109119125.784467627682-6.7844676276823
110118129.416653420513-11.4166534205128
111113120.113811035301-7.1138110353006
112123118.8066989426344.19330105736555
113142133.4540286061238.54597139387727
114141133.3033641130047.6966358869957
115138129.2925495559858.70745044401522
116124125.713429896508-1.71342989650771
11783100.003562887558-17.0035628875582
118100108.310988013908-8.3109880139077
11996104.220695108887-8.22069510888707
1209897.74930866496630.250691335033650







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12184.925628675058972.097551186288297.7537061638295
12292.352341583321576.4068273587536108.297855807889
12392.590680913940674.0425916736461111.138770154235
12499.473693687148378.6439991873445120.303388186952
125112.15581751213889.2692902851702135.042344739106
126105.47167416622680.6970397533869130.246308579066
12796.035870256304469.5058052837184122.565935228890
12883.308929113101555.1313020102517111.486556215951
12954.875546569224825.140289641801284.6108034966483
13077.988437021058846.7720169382773109.204857103840
13180.052812759676547.4212814894648112.684344029888
13281.85246591164747.8636238534155115.841307969879

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 84.9256286750589 & 72.0975511862882 & 97.7537061638295 \tabularnewline
122 & 92.3523415833215 & 76.4068273587536 & 108.297855807889 \tabularnewline
123 & 92.5906809139406 & 74.0425916736461 & 111.138770154235 \tabularnewline
124 & 99.4736936871483 & 78.6439991873445 & 120.303388186952 \tabularnewline
125 & 112.155817512138 & 89.2692902851702 & 135.042344739106 \tabularnewline
126 & 105.471674166226 & 80.6970397533869 & 130.246308579066 \tabularnewline
127 & 96.0358702563044 & 69.5058052837184 & 122.565935228890 \tabularnewline
128 & 83.3089291131015 & 55.1313020102517 & 111.486556215951 \tabularnewline
129 & 54.8755465692248 & 25.1402896418012 & 84.6108034966483 \tabularnewline
130 & 77.9884370210588 & 46.7720169382773 & 109.204857103840 \tabularnewline
131 & 80.0528127596765 & 47.4212814894648 & 112.684344029888 \tabularnewline
132 & 81.852465911647 & 47.8636238534155 & 115.841307969879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79439&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]84.9256286750589[/C][C]72.0975511862882[/C][C]97.7537061638295[/C][/ROW]
[ROW][C]122[/C][C]92.3523415833215[/C][C]76.4068273587536[/C][C]108.297855807889[/C][/ROW]
[ROW][C]123[/C][C]92.5906809139406[/C][C]74.0425916736461[/C][C]111.138770154235[/C][/ROW]
[ROW][C]124[/C][C]99.4736936871483[/C][C]78.6439991873445[/C][C]120.303388186952[/C][/ROW]
[ROW][C]125[/C][C]112.155817512138[/C][C]89.2692902851702[/C][C]135.042344739106[/C][/ROW]
[ROW][C]126[/C][C]105.471674166226[/C][C]80.6970397533869[/C][C]130.246308579066[/C][/ROW]
[ROW][C]127[/C][C]96.0358702563044[/C][C]69.5058052837184[/C][C]122.565935228890[/C][/ROW]
[ROW][C]128[/C][C]83.3089291131015[/C][C]55.1313020102517[/C][C]111.486556215951[/C][/ROW]
[ROW][C]129[/C][C]54.8755465692248[/C][C]25.1402896418012[/C][C]84.6108034966483[/C][/ROW]
[ROW][C]130[/C][C]77.9884370210588[/C][C]46.7720169382773[/C][C]109.204857103840[/C][/ROW]
[ROW][C]131[/C][C]80.0528127596765[/C][C]47.4212814894648[/C][C]112.684344029888[/C][/ROW]
[ROW][C]132[/C][C]81.852465911647[/C][C]47.8636238534155[/C][C]115.841307969879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79439&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12184.925628675058972.097551186288297.7537061638295
12292.352341583321576.4068273587536108.297855807889
12392.590680913940674.0425916736461111.138770154235
12499.473693687148378.6439991873445120.303388186952
125112.15581751213889.2692902851702135.042344739106
126105.47167416622680.6970397533869130.246308579066
12796.035870256304469.5058052837184122.565935228890
12883.308929113101555.1313020102517111.486556215951
12954.875546569224825.140289641801284.6108034966483
13077.988437021058846.7720169382773109.204857103840
13180.052812759676547.4212814894648112.684344029888
13281.85246591164747.8636238534155115.841307969879



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')